Question

CSATHardPrelims 2024Reasoning

In some code, letters P, Q, R, S, T represent numbers 4, 5, 10, 12, 15. It is not known which letter represents which number. If $Q - S = 2S$ and $T = R + S + 3$ , then what is the value of $P + R - T$ ?

Explanation

We have two conditions:

$Q – S = 2S$ , which simplifies to $Q = 3S$ .
$T = R + S + 3$ .

Step 1: Analyze the possible values for S and Q

From $Q = 3S$ $Q = 3 S$ , we can deduce that Q must be a multiple of 3.
- If $S = 5$ , then $Q = 15$ .
- If $S = 4$ , then $Q = 12$ .

Step 2: Case (1) $S = 4$ and $Q = 12$

$T = R + S + 3 \Rightarrow T = R + 7$
$T = 12$ and $R = 5$ , which contridicts with $Q = 12$ . So, this case is invalid.

Case (2) $S = 5$ and $Q = 15$

From $T = R + S + 3$ $T = R + S + 3$ , we substitute $S = 5$ $S = 5$ :
- $T = R + 5 + 3 = R + 8$ .
Now, the possible values for T and R are 4, 10, 12, and 15.
- If $T = 12$ , then $R = 12 – 8 = 4$ .
So, we have $R = 4$ , $S = 5$ , $T = 12$ , $Q = 15$ .
The remaining number is 10, so $P = 10$ .